Question

1. The ratio of the exterior angle to the interior angle of a regular polygon is 1:3 . Find the number of sides of the polygon ​

Answer 1

n=8

Solution,

Interior angle of regular polygon of n sides:

`((n - 2)180)/(n)`

Exterior angle of regular polygon of n sides:

`(360)/(n)`

Given,

`( (360)/(n) )/( ((n - 2)180)/(n) ) = (1)/(3) \\ or \: (360)/((n - 2)180) = (1)/(3) \\ or \: (360)/(180n - 360) = (1)/(3) \\ or \: 180n - 360 = 360 * 3 \\ or \: 180n - 360 = 1080 \\ or \: 180n = 1080 + 360 \\ or \: 180n = 1440 \\ or \: n = (1440)/(180) \\ n = 8`

Hope this helps...

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